Sketching Quadratic Graphs from Roots and the Turning Point · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Sketching Quadratic Graphs from Roots and the Turning Point

Mathematics · Algebra · ages 15-16
Name ______________________   Date ____________

  1. What is the value of the turning point of y = x squared - 10x + 21?

    • -4
    • 4
    • 21
    • -21

  2. In y = x squared - 3x + 8, what is the y-intercept?

    Answer: ______________

  3. In the form (x - 4) squared - 7, what is the x-coordinate of the turning point?

    Answer: ______________

  4. The line of symmetry of y = x squared - 2x + 5 is x = 1.

    Circle one:   True   False

  5. In y = -3x squared + 5x - 2, what is the x-coordinate of the line of symmetry? Give your answer to 2 decimal places.

    Answer: ______________

  6. Ava says the curve y = (x - 2) squared + 3 crosses the x-axis twice. Is she right?

    Circle one:   True   False

  7. Which choice gives both roots of y = x squared + 8x + 12?

    • 2 and 6
    • -2 and 6
    • 2 and -6
    • -2 and -6

  8. What is the maximum value of y = -x squared + 6x - 5?

    • 3
    • 6
    • 4
    • -5

  9. Ben describes the curve y = -x squared + 2x - 3 as always above the x-axis, never touching it. Which description is actually correct?

    • it crosses the axis twice
    • it is always above the axis
    • it never touches the axis and stays below it
    • it touches the axis once

  10. A curve in the form y = (x - a) squared + b crosses the x-axis at 2 and 6. What is a?

    • 4
    • -4
    • 2
    • 6
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Answer key

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Sketching Quadratic Graphs from Roots and the Turning Point W1-mt_RcrJIbbN2x-s1

  1. -4 · Completing the square gives (x - 5) squared - 4, so the turning point value is -4.
  2. 8 · The y-intercept is c, which is 8.
  3. 4 · In (x + p) squared + q the turning point x-coordinate is -p. Here p is -4, so -p is 4.
  4. True · The line of symmetry is x = -b over 2a, which is 2 over 2, giving x = 1.
  5. 0.83 · The line of symmetry is x = -b over 2a, which is -5 over -6, about 0.83.
  6. False · The turning point value is +3, above the axis, and the U opens upward, so the curve never reaches the axis.
  7. -2 and -6 · x squared + 8x + 12 factorises to (x + 2)(x + 6), so the roots are -2 and -6.
  8. 4 · Completing the square gives -(x - 3) squared + 4, so the maximum value is 4.
  9. it never touches the axis and stays below it · The discriminant is 4 - 12, which is -8, so it never touches the axis, and the negative x squared coefficient means it opens downward, below the axis.
  10. 4 · The line of symmetry is halfway between the roots, at x = 4, and in (x - a) squared + b it is x = a.
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